Quantum Secret Sharing

Functionality Description

Quantum Secret Sharing (QSS) allows to transfer a quantum state (or a classical message encoded as quantum state), referred to as the secret, from Alice to Bob but only with the consent of a third-party, Charlie. A QSS protocol is generalizable to an arbitrary number of parties consisting of one sender, one recipient, and all other parties being endorsers. In case of only two parties, sender and receiver, QSS is equivalent to Quantum Teleportation. Despite the no-cloning theorem not allowing the quantum secret to be in possession of more than one party at the same time, there exist QSS protocols that mimic classical secret sharing (see Further Information).

Tags: Building Blocks, Multi Party, Quantum Enhanced Classical Functionality

Use Cases

• QSS can replace certain classical secret sharing scenarios with unconditional security.(1)
• Secret sharing is a very common building block in other protocols:(2)
  • Secure Multiparty Delegated Quantum Computation
  • Leader election and Byzantine Agreement
  • Error correction in quantum computers(3)
  • Bank transfers with third party endorsement, see Quantum Cheque

Protocols

1. Quantum Secret Sharing using GHZ States(4)
2. Verifiable Quantum Secret Sharing (VQSS)

Properties

• Confidentiality: QSS with one dishonest party not following the protocol must guarantee that no information about the quantum secret at all is revealed to any party.
• Security: Every protocol must ensure that no information about the secret is leaked to an external eavesdropper.

Further Information

QSS is inspired by classical secret sharing (CSS), but has one fundamental difference due to the no-cloning theorem. In CSS, Alice shares a secret among $n$ parties and any team of $t$ parties or more, with $t\leq n$, has full access to the secret, whereas $t-1$ collaborating parties or less have no information about the secret at all. Such $(t,n)$-threshold schemes are not straightforward to implement for QSS, since the no-cloning theorem forbids that quantum states are copied, resulting in only one party, the receiver, obtaining the quantum secret from Alice, who looses hers during the process. However, $(t,n)$ schemes can be built through sequentially running several QSS rounds.(5)

References

1. Mayers (2001)
2. Joy et al (2018)
3. Gottesman (1999)
4. Hillery et al (1998)
5. Lu et al (2018)

contributed by Peter Limacher